With the one exception these are stories rather than picturebooks, but they have small and simple but charming black, white, red and yellow illustrations. (These are also, like the rest of the New York Review Children's Collection, physically lovely volumes which make great presents.) They have engaging characters and plots, and are suitable for children old enough to understand the social interactions — the publisher's guidelines are 3-7 and 5-9. My four year old loved them. They also have simple language and largish print and should work well for early readers.
Jenny and the Cat Club: A Collection of Favourite Stories About Jenny Linsky contains five stories, each thirty two pages long. These all have social themes: how Jenny is accepted into the cat club, how she copes with going to a party and being ignored, what happens when she loses her favourite scarf, and how she copes with Captain Tinker adopting two more cats. Jenny's Moonlight Adventure and A School for Cats contain single stories of the same length: in the first Jenny has to brave the neighbourhood dogs to help out a member of the club; in the second she goes to school for the first time and has to deal with a bully. Jenny's Birthday Book is more of a picturebook, with bigger illustrations and more colours, less text, and a simple feel-good story.
Jenny Goes to Sea is a short novel, running to 140 pages, but is relatively accessible, with an episodic story arc involving adventures in different ports of call and with a central cast of four: Jenny and her brothers and the ship's cat Jack Tar. My four year old was happy for me to read it to her, but neither she nor I found it as compelling as the short stories. (There are two other Cat Club novels, The Hotel Cat and Captains of the City Streets, but these are 170 page novels pitched at older children, with a publisher recommended age of 10-14; they were also written over a decade after the other stories.)
Of these books Jenny and the Cat Club is the best starting point, since it contains the introductory story and four others and is only marginally more expensive than the single story books. Jenny's Birthday Book is aimed at slightly younger children, but it lacks the plot interest of the other stories and will work best for those who already know the characters. (There is also an "I Can Read" early reader book, The Fire Cat, which I am saving for learning to read.)
Update: I read The Hotel Cat and Captains of the City Streets to my daughter six months after this, a little before she turned five. She read them herself just after she turned seven.